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What we cannot learn from analogue experiments

  • S.I.: Reasoning in Physics
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Abstract

Analogue experiments have attracted interest for their potential to shed light on inaccessible domains. For instance, ‘dumb holes’ in fluids and Bose–Einstein condensates, as analogues of black holes, have been promoted as means of confirming the existence of Hawking radiation in real black holes. We compare analogue experiments with other cases of experiment and simulation in physics. We argue—contra recent claims in the philosophical literature—that analogue experiments are not capable of confirming the existence of particular phenomena in inaccessible target systems. As they must assume the physical adequacy of the modelling framework used to describe the inaccessible target system, arguments to the conclusion that analogue experiments can yield confirmation for phenomena in those target systems, such as Hawking radiation in black holes, beg the question.

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Notes

  1. Wüthrich (forthcoming) offers an analysis of Bekenstein’s argument and an assessment of the strength of the analogy he argues for, arriving at a largely negative conclusion concerning Bekenstein’s original case. Dougherty and Callender (forthcoming) and Wallace (2017) undertake a more general evaluation of the strength of the analogy, and reach opposing conclusions.

  2. Note, however, that physicists are premature in accepting the hypothetical temperature of Hawking radiation as being an actual temperature—and thereby in promoting the analogy between thermodynamics and black holes to an identity.

  3. We will use the term ‘inaccessible’ in a non-technical sense throughout, hoping that, whatever its precise characterisation, it should be clear that astrophysical black holes are experimentally inaccessible.

  4. This is not the only work on this: for example, Rousseaux et al. (2008), Rousseaux et al. (2010), Weinfurtner et al. (2013) and Euvé et al. (2016) (among others) had indeed already found the analogue Hawking effect in fluid systems (using water tanks). These analogue systems can however only mimic stimulated Hawking radiation (sometimes referred to as the ‘classical Hawking effect’) as opposed to spontaneous Hawking radiation (as in Steinhauer’s experiment). As gravitational Hawking radiation can only be spontaneous, Steinhauer’s finding allows for the stronger analogy.

  5. Since the confirmation these authors are seeking is of course inductive rather than deductive, we do not accuse them of committing the fallacy of deductive reasoning known under the same name. However, we do accuse them of an inductive analogue of that fallacy and thus use the same expression.

  6. We take ‘analogue’ to be synonymous with ‘analogical’.

  7. See Bartha (2010, §8.5; 2016, §2.3), and, for a rather positive account on the linkage between confirmation and analogical argument, Hesse (1964).

  8. This distinction is akin to one that has frequently been proposed to distinguish experiments from simulations, which holds that, in experiments, S and T bear material similarities, while in simulations, S and T bear only formal similarities. We agree with Winsberg (2009, 2010) that a distinction along these lines is not tenable, whether between simulations and experiments, or analogue- and non-analogue experiments.

  9. Cf. Batterman (2000).

  10. Admittedly, this has apparently been explored more in the context of biology, e.g., Baetu (2016), Weber (2018, §3), and in the literature on simulation, e.g., Winsberg (2010).

  11. Note that DTW do not themselves suggest that the syntactic isomorphism is the defining feature of analogue experiments, nor that its use is sufficient for distinguishing an analogue experiment from a conventional one.

  12. This is of course not the only aim or benefit of these experiments! But, as we argue in Sect. 4, according to DTW, if dumb holes are to be confirmatory of black hole phenomena, it is precisely this universality that must be established.

  13. We of course acknowledge the difference between an argument and an experiment, but our point is that analogical arguments are still analogical arguments even when they relate to concrete, manipulable systems in the world.

  14. In a nutshell, this is also the reason why we will come to the conclusion in the following sections that dumb holes and other currently available analogue experiments on Hawking radiation simply cannot confirm the existence of gravitational Hawking radiation.

  15. Winsberg (2009, 2010) for instance characterises the distinction between simulation and experiment epistemically; for a simulation or experiment to be externally valid, S (in either case) is hoped to “stand in” for T, by sharing formal descriptions, and in both cases this hope is justified by various background knowledge and assumptions of the researchers. In the case of experiment, this background is, for instance, the belief that S and T are the same kind of system, perhaps being materially similar. By contrast, in the case of simulation, the background is based on certain features of model building practices (background knowledge about model building practices is also used in the case of experiment, but according to Winsberg, the difference here is that in experiment this is mainly used to establish internal validity, while in the case of simulation it concerns external validity). Thus, on Winsberg’s account of simulation, it is possible that S and T are supposed to be the same kind of system, but this supposition is not what is used to justify the belief in the external validity of the simulation.

  16. Cf. also DTW (2017) and Thébault (forthcoming).

  17. Hawking radiation has been derived for other kind of fields, including the electrodynamical vector field, although not necessarily using an analogous derivation. In fact, there seem to be at least five (putatively) independent derivations of the Hawking effect in the literature [cf. Wallace (2017)].

  18. It does not require a framework of semi-classical gravity in the sense of accounting for the backreaction of quantum matter to spacetime.

  19. In other words, the exact same limit behaviour might be reproducible by myriad theories other than QFTs in curved spacetime.

  20. For an introduction to the topic of inflation, including the derivation of primordial density fluctuations, see e.g., Baumann (2011). For experimental results on the spectrum see Crotty et al. (2003).

  21. See for instance Lanusse et al. (2014).

  22. Consider for instance Brandenberger (2014, p. 118) on this:

    However, the physics of the generation mechanism is very different. In the case of inflationary cosmology, fluctuations are assumed to start as quantum vacuum perturbations because classical inhomogeneities are red-shifting. In contrast, in the Hagedorn phase of string gas cosmology there is no red-shifting of classical matter. Hence, it is the fluctuations in the classical matter which dominate. Since classical matter is a string gas, the dominant fluctuations are string thermodynamic fluctuations.

  23. Bose–Einstein condensates can be treated at the level of a hydrodynamic approximation, see Garay et al. (2000).

  24. We are following Thébault (forthcoming) here.

  25. These calculations are further discussed in DTW and Thébault regarding the trans-Planckian problem, but this is not important for our arguments.

  26. This reading is supported, e.g., by DTW’s use of the idea of ‘universality’, and statements like, “we defend the claim that the phenomena of gravitational Hawking radiation could be confirmed in the case its counterpart is detected within experiments conducted on diverse realizations of the analogue model.” Dardashti et al. (2017, p. 55)

  27. Something Bekenstein failed to do, as argued in Wüthrich (forthcoming).

  28. In the case of Hawking radiation (there are other trans-Planckian problems, e.g., the trans-Planckian problem in inflation), Unruh and Schützhold characterise the issue as follows: “in view of the (exponential) gravitational red-shift near the horizon, the outgoing particles of the Hawking radiation originate from modes with extremely large (e.g., trans-Planckian) wavenumbers. As the known equations of quantum fields in curved space-times are expected to break down at such wavenumbers, the derivation of the Hawking radiation has the flaw that it applies a theory beyond its region of validity. This observation poses the question of whether the Hawking effect is independent of Planckian physics or not.” (p. 1)

  29. DTW (mistakenly) leave out the first of these four conditions (see quote of DTW above)—probably because these are not made so explicit by Unruh and Schützhold as are the other three conditions [referred to as (i)–(iii)].

  30. More precisely, Unruh and Schützhold’s assumption of a (preferred) freely falling frame at high energies explicitly breaks (local) Lorentz invariance:

    If we assume that the usual local Lorentz invariance is broken at the Planck scale via the introduction of preferred frames (where preferred frames are the frames in which Planckian physics displays maximal symmetry under time-inversion, for example) then the freely falling frame should be preferred (instead of the rest frame of the black hole, for example). (p. 9)

  31. See Footnote 5.

  32. “From our perspective, if it proves that a philosophical model of confirmation cannot accommodate confirmation via analogue simulation at all, then this would be as much a problem for the model, as it would for analogue simulation.” (DTW 2017, p. 12).

  33. Even gravitational Hawking radiation cannot serve in a straightforward confirmation of QFT in a curved spacetime: as Hawking radiation can only be derived in a ‘QFT in curved spacetime’ setting under further assumptions on the high-energy physics (to evade the prominent trans-Planckian problem), any test of it is in fact a test of both (1) the applicability of the QFT in curved spacetime framework, and (2) any proposed trans-Planckian physics behaviour used to evade the trans-Planckian problem (that the Hawking radiation needs to involve a cut-off of higher than Planck-scale energy behaviour), i.e., Hawking radiation can only serve as a test for both at the same time.

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Acknowledgements

We thank audiences in Bad Honnef, Seven Pines, Geneva, Salzburg, Dubrovnik, and Bern, as well as Radin Dardashti, Karim Thébault, and Marcel Weber for discussions. We also thank the two referees for their careful and patient engagement with our paper. We acknowledge financial support (for K.C. and N.L.) from the Swiss National Science Foundation (Project 105212_165702) and (for C.W.) from the John Templeton Foundation (Grant 56314, made under a collaborative agreement between the University of Illinois at Chicago and the University of Geneva). The content of this work are solely the responsibility of the authors and do not represent the official views of the Swiss National Science Foundation or the John Templeton Foundation.

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  1. Philosophy Department, University of Geneva, 2 rue de Candolle, 1211, Geneva 4, Switzerland

    Karen Crowther, Niels S. Linnemann & Christian Wüthrich

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  1. Karen Crowther
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Correspondence to Niels S. Linnemann.

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Crowther, K., Linnemann, N.S. & Wüthrich, C. What we cannot learn from analogue experiments. Synthese 198 (Suppl 16), 3701–3726 (2021). https://doi.org/10.1007/s11229-019-02190-0

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